Significance: Headwater streams account for a majority of river networks worldwide and have a disproportionately large influence on the functioning of aquatic ecosystems. Headwater streams also support critical habitat for many species, including cold-water fishes, many of which are declining or at risk of extinction.
Problem: Headwater streams are largely underrepresented in streamflow monitoring networks, which place greater emphasis on mainstem rivers. As a result, less is known about how headwaters respond to changing water availability. Headwater streams therefore represent a blind spot in understanding flow regime variability and assessing the vulnerability of cold-water fish to changing climatic conditions, including the increasing frequency and severity of drought.
Existential question: How do streamflow regimes vary spatially in headwater stream networks and what does this imply about the sensitivity of these systems (and the species they support) to changing climatic conditions (i.e., drought)?
Objectives:
Evaluate the extent and magnitude of spatial and temporal variation in headwater streamflow.
Visualize time series data to show difference in streamflow regimes between reference gages (big G/NWIS) and upstream gages (little g’s). Use CVPE to summarize the magnitude of the portfolio effect in headwater flow regimes.
Back up with ridgeline plots and exceedance curves to describe spatial diversity in distribution of flow values, generally (at monthly time scales and within the “dry” season, respectively)
Explore non-linear and hysteretic relationship between flow at reference vs. at headwater gages
Trim data to complete site-years and use scatterplots to show diversity in g~G relationships within and among basins.
Conduct event delineation and calculate the (modified) Lloyd index for each g~G pair of storms. Arrange sites on a frequency/magnitude bi-plot and highlight differences among (rain-snow) basins.
Quantify the suitability of existing modeling techniques for predicting streamflow in headwater systems.
Use NSE (Nash-Sutcliffe efficiency) to compare the performance of Stream Stats, PRMS (in the Donner-Blitzen only), and Hoyleman’s neural net model to understand the utility of existing tools for modeling headwater streamflow. (How well do these tools perform when applied to catchments smaller than those used paramertize each tool?)
Maybe this is a box or a discussion point?
Demonstrate how drought-related low flow conditions manifest differently in streams across headwater networks.
Using site-specific low flow thresholds derived from contemporary data (sensu Hammond et al. 2022), show how streamflow drought duration and deficit vary among headwater streams and relative to big G (heatmaps and barplots)
Explore how network heterogeneity changes with threshold magnitude and among years that differ in regional water availability (scatterplots)
Conceptual Model: develop a conceptual framework and set of hypotheses based on the objectives above How do we link/combine what we have learned so far to enhance our understanding of spatial diversity in headwater streamflow regimes?
Moving beyond “The Natural Flow Regime” - understanding and quantifying flow regime diversity in headwater stream networks
Perhaps the fluvial synchrogram concept will be helpful as a starting point. Also see Scholl et al. (in review) and Rossi et al. (2024) for inspiration
Boxes: Use boxes to highlight additional details of the data, vignettes, and case studies that demonstrate spatiotemporal streamflow heterogeneity
High temporal resolution data reveals network diverse in streamflow response to individual storms and during low flow
Show sub-daily/hourly flow data for selected storms and baseflow periods (diurnal cycles during very low flows) to show heterogeneity at very fine temporal resolutions
The Wedge Hypothesis/model for rain-dominated basins (West Brook)
Fit the basic wedge model for the West Brook…and develop hypotheses for how this would play out in snow-dominated basins (bowtie hypothesis)
What does this this tell us about how diversity in flow regimes is driven by climate regime, antecedent conditions, and catchment storage capacity? See Dralle et al. (2023)
Synoptic surveys reveal super fine-scale spatial variation in flow at a single point in time. (perhaps separate boxes for DB and Shen)
Donner-Blitzen: longitudinal temperature and flow surveys and aerial thermal imagery show how localized groundwater inflow from geologic faults drives abrupt changes in stream conditions. (Christian Torgersen, Brandon Overstreet)
Shanandoah: dewatering surveys show how longitudinal flow variability can affect habitat connectivity within headwater streams, but this is mediated by catchment characteristics and changing regional water availability among years. See Hitt et al. (2024). (Karli Rogers, Than Hitt). Could show relationship between size of largest patch (or number of patches, distribution of patch sizes) and regional annual water availability (or flow at big G/UVA gages).
Effects of groundwater on relative flow within basins.
Show the effect of groundwater availability (derived from PASTA) on mean summer flow (or distribution of summer values).
This could be combined with the above box(es), but is potentially less powerful. Low priority
# flow/yield (and temp) data dat <-read_csv("C:/Users/jbaldock/OneDrive - DOI/Documents/USGS/EcoDrought/EcoDrought Working/Data/EcoDrought_FlowTempData_DailyWeekly.csv") %>%mutate(site_name = dplyr::recode(site_name, "Leidy Creek Mouth NWIS"="Leidy Creek Mouth", "SF Spread Creek Lower NWIS"="SF Spread Creek Lower", "Dugout Creek NWIS"="Dugout Creek", "Shields River ab Smith NWIS"="Shields River Valley Ranch")) %>%filter(!site_name %in%c("Avery Brook NWIS", "West Brook 0", "BigCreekMiddle", # drop co-located sites"South River Conway NWIS", "North Fork Flathead River NWIS", # drop big Gs"Pacific Creek at Moran NWIS", "Shields River nr Livingston NWIS", # drop big Gs"Donner Blitzen River nr Frenchglen NWIS", # drop big Gs"WoundedBuckCreek")) %>%# drop little g outside of focal basingroup_by(site_name, basin, subbasin, region, date) %>%summarize(flow_mean =mean(flow_mean),tempc_mean =mean(tempc_mean),Yield_mm =mean(Yield_mm),Yield_filled_mm =mean(Yield_filled_mm)) %>%ungroup()# add water/climate year variables and fill missing datesdat <-fill_missing_dates(dat, dates = date, groups = site_name)dat <-add_date_variables(dat, dates = date, water_year_start =10)
Clean and bind little g data (for each basin, restrict to time period for which data quality/availability is ~consistent)
Code
dat_clean <-bind_rows( dat %>%filter(site_name %in%unlist(siteinfo %>%filter(subbasin =="West Brook") %>%select(site_name)), year(date) >=2020, date <=date("2025-01-03")) %>%mutate(Yield_filled_mm =ifelse(site_name =="West Brook Upper"& date >date("2024-10-06"), NA, Yield_filled_mm)) %>%mutate(Yield_filled_mm =ifelse(site_name =="Mitchell Brook"& date >date("2021-02-28") & date <date("2021-03-26"), NA, Yield_filled_mm)) %>%mutate(Yield_filled_mm =ifelse(site_name =="Mitchell Brook"& date >date("2021-11-01") & date <date("2022-05-01"), NA, Yield_filled_mm)) %>%mutate(Yield_filled_mm =ifelse(site_name =="Jimmy Brook"& date >date("2024-12-10"), NA, Yield_filled_mm)) %>%mutate(subbasin ="West Brook"), dat %>%filter(site_name %in%unlist(siteinfo %>%filter(subbasin =="Paine Run") %>%select(site_name)), date >=as_date("2018-11-07"), date <=as_date("2023-05-15")) %>%mutate(subbasin ="Paine Run"), dat %>%filter(site_name %in%unlist(siteinfo %>%filter(subbasin =="Staunton River") %>%select(site_name)), date >=as_date("2018-11-07"), date <=as_date("2022-10-19")) %>%mutate(subbasin ="Staunton River"), dat %>%filter(site_name %in%c(unlist(siteinfo %>%filter(subbasin =="Big Creek") %>%select(site_name)), "North Fork Flathead River NWIS"), date >=date("2018-08-08"), date <=date("2023-08-03"), site_name !="SkookoleelCreek", Yield_filled_mm >0) %>%mutate(subbasin ="Big Creek"), dat %>%filter(site_name %in%c(unlist(siteinfo %>%filter(subbasin =="Coal Creek") %>%select(site_name)), "North Fork Flathead River NWIS"), date >=date("2018-07-29"), date <=date("2023-08-03")) %>%mutate(subbasin ="Coal Creek"), dat %>%filter(site_name %in%c(unlist(siteinfo %>%filter(subbasin =="McGee Creek") %>%select(site_name)), "North Fork Flathead River NWIS"), date >=date("2017-07-30"), date <=date("2023-12-11")) %>%mutate(subbasin ="McGee Creek"), dat %>%filter(subbasin =="Snake River", date >=date("2016-04-01"), date <=date("2023-10-03"), site_name !="Leidy Creek Upper") %>%mutate(subbasin ="Snake River"), dat %>%filter(subbasin =="Shields River", date >=date("2016-04-01"), date <=date("2023-12-31"), site_name !="Brackett Creek") %>%mutate(logYield =log10(Yield_filled_mm)) %>%mutate(subbasin ="Shields River"), dat %>%filter(subbasin =="Duck Creek", date >=date("2015-04-01"), date <=date("2023-12-31")) %>%mutate(subbasin ="Duck Creek"), dat %>%filter(subbasin =="Donner Blitzen", date >=as_date("2019-04-23"), date <=as_date("2022-12-31"), !site_name %in%c("Indian Creek NWIS", "Little Blizten River NWIS")) %>%mutate(subbasin ="Donner Blitzen")) %>%filter(Yield_filled_mm >0) %>%mutate(logYield =log10(Yield_filled_mm), designation ="little", doy_calendar =yday(date)) %>%select(-Yield_mm) %>%rename(Yield_mm = Yield_filled_mm)head(dat_clean)
# A tibble: 6 × 16
site_name basin subbasin region date flow_mean tempc_mean Yield_mm
<chr> <chr> <chr> <chr> <date> <dbl> <dbl> <dbl>
1 Avery Brook West Bro… West Br… Mass 2020-01-08 5.96 0.594 1.99
2 Avery Brook West Bro… West Br… Mass 2020-01-09 4.81 0.0336 1.61
3 Avery Brook West Bro… West Br… Mass 2020-01-10 4.88 0.363 1.63
4 Avery Brook West Bro… West Br… Mass 2020-01-11 6.43 1.77 2.15
5 Avery Brook West Bro… West Br… Mass 2020-01-12 21.2 2.81 7.08
6 Avery Brook West Bro… West Br… Mass 2020-01-13 14.3 1.92 4.78
# ℹ 8 more variables: CalendarYear <dbl>, Month <dbl>, MonthName <fct>,
# WaterYear <dbl>, DayofYear <dbl>, logYield <dbl>, designation <chr>,
# doy_calendar <dbl>
11.1.2 Big G’s
Load big/super G data
Code
nwis_daily <-read_csv("C:/Users/jbaldock/OneDrive - DOI/Documents/USGS/EcoDrought/EcoDrought Working/Data/EcoDrought_NWIS_FlowTempData_Raw_Daily.csv") %>%filter(designation =="big", year(date) >=1970, site_name !="Shields River nr Livingston NWIS") %>%mutate(flowcfs =ifelse(site_name =="Rapidan River NWIS"& date >date("1995-06-26") & date <date("1995-07-01"), NA, flowcfs),flow_mean_cms = flowcfs*0.02831683199881, area_sqkm = area_sqmi*2.58999)# sitessites <-unique(nwis_daily$site_name)# site-specific basin area in square kmbasinarea <- nwis_daily %>%filter(!is.na(site_id)) %>%group_by(site_name) %>%summarize(area_sqkm =unique(area_sqkm))# calculate yieldyield_list <-list()for (i in1:length(sites)) { d <- nwis_daily %>%filter(site_name == sites[i]) ba <-unlist(basinarea %>%filter(site_name == sites[i]) %>%select(area_sqkm)) yield_list[[i]] <-add_daily_yield(data = d, values = flow_mean_cms, basin_area =as.numeric(ba))}nwis_daily_wyield <-do.call(rbind, yield_list)dat_clean_big <- nwis_daily_wyield %>%select(site_name, basin, subbasin, region, date, Yield_mm, tempc, flowcfs) %>%mutate(logYield =log10(Yield_mm), doy_calendar =yday(date)) %>%rename(tempc_mean = tempc, flow_mean = flowcfs)# add water/climate year variables and fill missing datesdat_clean_big <-fill_missing_dates(dat_clean_big, dates = date, groups = site_name)dat_clean_big <-add_date_variables(dat_clean_big, dates = date, water_year_start =10)head(dat_clean_big)
# A tibble: 6 × 15
site_name basin subbasin region date Yield_mm tempc_mean flow_mean
<chr> <chr> <chr> <chr> <date> <dbl> <dbl> <dbl>
1 South River Co… West… West Br… Mass 1970-01-01 1.81 NA 46
2 South River Co… West… West Br… Mass 1970-01-02 1.69 NA 43
3 South River Co… West… West Br… Mass 1970-01-03 1.61 NA 41
4 South River Co… West… West Br… Mass 1970-01-04 1.53 NA 39
5 South River Co… West… West Br… Mass 1970-01-05 1.49 NA 38
6 South River Co… West… West Br… Mass 1970-01-06 1.49 NA 38
# ℹ 7 more variables: logYield <dbl>, doy_calendar <dbl>, CalendarYear <dbl>,
# Month <dbl>, MonthName <fct>, WaterYear <dbl>, DayofYear <dbl>
Download Daymet precip data and summarize by water year
Code
# big G site lat/longmysites <- nwis_daily %>%group_by(site_name, basin, subbasin, region) %>%summarize(lat =unique(lat), long =unique(long)) %>%ungroup()# download point location Daymet dataclimlist <-vector("list", length =dim(mysites)[1])for (i in1:dim(mysites)[1]) { clim <-download_daymet(site = mysites$site_name[i], lat = mysites$lat[i], lon = mysites$long[i], start =1980, end =2024, internal = T) climlist[[i]] <-tibble(clim$data) %>%mutate(air_temp_mean = (tmax..deg.c. + tmin..deg.c.)/2, date =as.Date(paste(year, yday, sep ="-"), "%Y-%j"),site_name = mysites$site_name[i]) %>%select(12,2,11,10,4,6) %>%rename(precip_mmday =5, swe_kgm2 =6)print(i)}
[1] 1
[1] 2
[1] 3
[1] 4
[1] 5
[1] 6
[1] 7
[1] 8
Code
# combine and add water yearsclimdf <-do.call(rbind, climlist) %>%left_join(mysites) %>%mutate(year =year(date))climdf <-add_date_variables(climdf, dates = date, water_year_start =10)# calculate total annual precipitation in mm, by site and water yearclimdf_summ <- climdf %>%group_by(site_name, basin, subbasin, region, WaterYear) %>%summarize(precip_total =sum(precip_mmday), sampsize =n()) %>%mutate(precip_total_z =scale(precip_total)) %>%ungroup() %>%filter(sampsize >=350)
View time series and scatter plots of big G water availability (total annual yield, sum of daily values, black lines) and precipitation (total annual precip, blues lines). Note that the panel labels indicate basins, not NWIS gage names. In the manuscript, pair these plots with CONUS map and detailed inset maps of focal basins (Figure 1)
Code
# calculate annual water availability at big g as sum of daily yield values...retain only years with >95% data coverage (at least 350 days)wateravail <- dat_clean_big %>%filter(!is.na(Yield_mm)) %>%group_by(basin, site_name, WaterYear) %>%summarize(sampsize =n(), totalyield =sum(Yield_mm, na.rm =TRUE)) %>%mutate(totalyield_z =scale(totalyield)[,1]) %>%ungroup() %>%filter(sampsize >=350) %>%complete(basin, WaterYear =1971:2024, fill =list(sampsize =NA, totalyield =NA))# get range of years for little g datadaterange <- dat_clean %>%group_by(basin) %>%summarize(minyear =year(min(date)), maxyear =year(max(date)))# spread ecod yearsmylist <-vector("list", length =dim(daterange)[1])for (i in1:dim(daterange)[1]) { mylist[[i]] <-tibble(basin = daterange$basin[i], WaterYear =seq(from = daterange$minyear[i], to = daterange$maxyear[i], by =1))}yrdf <-do.call(rbind, mylist) %>%mutate(ecodyr ="yes")
Objective 1: Evaluate the extent and magnitude of spatial and temporal variation in headwater streamflow.
Approach:
Visualize time series data to show difference in streamflow regimes between reference gages (big G/NWIS) and upstream gages (little g’s)
Back up with flow exceedance curves to describe spatial diversity in distribution of flow values, generally
Notes:
Consider combining subbasins
Flathead = Coal, Big, and McGee Creeks
Yellowstone = Shields River and Duck Creek
Shenandoah??? Hard b/c Staunton, Paine, and Piney all use different big G’s
Might be helpful to plot panels of static time series plot on the same x-axis/time scale
Not sure how necessary ridgeline plots are under the current framework/objectives, although they do highlight differences in variability between big and littls g’s
Exceedance curves need updating/doing, perhaps facet by year and restrict to summer/low flow season only (July, August, September).
11.2.1 Spaghetti plots
View daily time series data by sub-basin. Note that we are using the “Super G” NWIS data for the reference gage (black line). Per Robert comment, entirely nested design is cute, but doesn’t reflect how the data is actually used.
Big G NWIS sites/reference gages for each basin/subbasin:
myridgesfun(subbas ="West Brook", bigG ="South River Conway NWIS")
Code
myridgesfun(subbas ="Paine Run", bigG ="South River Harriston NWIS")
Code
myridgesfun(subbas ="Staunton River", bigG ="Rapidan River NWIS")
Code
myridgesfun(subbas ="Big Creek", bigG ="North Fork Flathead River NWIS")
Code
myridgesfun(subbas ="Coal Creek", bigG ="North Fork Flathead River NWIS")
Code
myridgesfun(subbas ="McGee Creek", bigG ="North Fork Flathead River NWIS")
Code
myridgesfun(subbas ="Snake River", bigG ="Pacific Creek at Moran NWIS")
Code
myridgesfun(subbas ="Shields River", bigG ="Yellowstone River Livingston NWIS")
Code
myridgesfun(subbas ="Duck Creek", bigG ="Yellowstone River Livingston NWIS")
Code
myridgesfun(subbas ="Donner Blitzen", bigG ="Donner Blitzen River nr Frenchglen NWIS")
11.3 Objective 2
Purpose: Explore non-linear and hysteretic relationship between flow at reference vs. at headwater gages
Approach:
Trim data to complete site-years.
Use scatterplots to show diversity in g~G relationships within and among basins.
Conduct event delineation and calculate the (modified) Lloyd index for each g~G pair of storms.
Arrange sites on a frequency/magnitude bi-plot and highlight differences among (rain-snow) basins.
11.3.1 Trim data
Find little g site/water years with at least 90% data completeness, join big and little g daily yield data
Code
# find little g site/water yeras with at least 90% data availabilitymysiteyrs <- dat_clean %>%group_by(site_name, basin, subbasin, region, WaterYear) %>%summarize(numdays =n(),totalyield_site =sum(Yield_mm)) %>%ungroup() %>%filter(numdays >=0.9*365) %>%mutate(forhyst =1) %>%left_join(wateravail %>%select(basin, WaterYear, totalyield_z))# join big G data to little gdat_clean_hyst <- dat_clean %>%left_join(mysiteyrs) %>%filter(forhyst ==1) %>%left_join(dat_clean_big %>%select(basin, date, Yield_mm, logYield) %>%rename(Yield_mm_big = Yield_mm, logYield_big = logYield)) %>%left_join(wateravail %>%select(basin, WaterYear, totalyield_z))# view datamysiteyrs
# A tibble: 87 × 9
site_name basin subbasin region WaterYear numdays totalyield_site forhyst
<chr> <chr> <chr> <chr> <dbl> <int> <dbl> <dbl>
1 Avery Brook West… West Br… Mass 2021 365 872. 1
2 Avery Brook West… West Br… Mass 2022 365 602. 1
3 Avery Brook West… West Br… Mass 2023 365 1147. 1
4 Avery Brook West… West Br… Mass 2024 345 993. 1
5 Big Creek NW… Flat… Big Cre… Flat 2019 329 566. 1
6 Big Creek NW… Flat… Big Cre… Flat 2020 347 719. 1
7 Big Creek NW… Flat… Big Cre… Flat 2021 352 554. 1
8 Big Creek NW… Flat… Big Cre… Flat 2022 340 842. 1
9 Buck Creek Shie… Shields… Shiel… 2022 329 174. 1
10 CycloneCreek… Flat… Coal Cr… Flat 2019 354 374. 1
# ℹ 77 more rows
# ℹ 1 more variable: totalyield_z <dbl>
Code
dat_clean_hyst
# A tibble: 30,889 × 22
site_name basin subbasin region date flow_mean tempc_mean Yield_mm
<chr> <chr> <chr> <chr> <date> <dbl> <dbl> <dbl>
1 Avery Brook West Br… West Br… Mass 2020-10-01 1.78 13.5 0.595
2 Avery Brook West Br… West Br… Mass 2020-10-02 1.02 12.5 0.341
3 Avery Brook West Br… West Br… Mass 2020-10-03 0.863 11.0 0.288
4 Avery Brook West Br… West Br… Mass 2020-10-04 0.654 10.0 0.218
5 Avery Brook West Br… West Br… Mass 2020-10-05 0.613 10.2 0.204
6 Avery Brook West Br… West Br… Mass 2020-10-06 0.628 11.1 0.209
7 Avery Brook West Br… West Br… Mass 2020-10-07 0.717 11.4 0.239
8 Avery Brook West Br… West Br… Mass 2020-10-08 0.787 10.7 0.262
9 Avery Brook West Br… West Br… Mass 2020-10-09 0.661 9.04 0.221
10 Avery Brook West Br… West Br… Mass 2020-10-10 0.734 9.95 0.245
# ℹ 30,879 more rows
# ℹ 14 more variables: CalendarYear <dbl>, Month <dbl>, MonthName <fct>,
# WaterYear <dbl>, DayofYear <dbl>, logYield <dbl>, designation <chr>,
# doy_calendar <dbl>, numdays <int>, totalyield_site <dbl>, forhyst <dbl>,
# totalyield_z <dbl>, Yield_mm_big <dbl>, logYield_big <dbl>
11.3.2 gG scatterplots
Create plotting function
Code
hystplotfun <-function(mysite, wy, months =c(1:12)) { (dat_clean_hyst %>%filter(site_name == mysite, WaterYear == wy, Month %in% months) %>%ggplot(aes(x = logYield_big, y = logYield, color = date)) +geom_segment(aes(xend =c(tail(logYield_big, n =-1), NA), yend =c(tail(logYield, n =-1), NA)), arrow =arrow(length =unit(0.2, "cm")), color ="black") +geom_point() +geom_abline(intercept =0, slope =1, linetype ="dashed") +scale_color_gradientn(colors =cet_pal(250, name ="c2"), trans ="date") +xlim(-1,1.5) +ylim(-1.5,1.8) +#scale_color_scico(palette = "romaO") +xlab("log(Yield, mm) at reference gage") +ylab("log(Yield, mm) at headwater gage") +# geom_text(data = annotations, aes(x = xpos, y = ypos, label = annotateText), hjust = "inward", vjust = "inward") +annotate(geom ="text", x =-Inf, y =Inf, label =paste(mysite, ", WY ", wy, sep =""), hjust =-0.1, vjust =1.5) +theme_bw() +theme(panel.grid.major =element_blank(), panel.grid.minor =element_blank(),panel.background =element_rect(fill ="grey85"),axis.title =element_blank()) +theme(plot.margin =margin(0.1,0.1,0,0, "cm")) )}# change to linear color palettehystplotfunlin <-function(mysite, wy, months =c(1:12)) { (dat_clean_hyst %>%filter(site_name == mysite, WaterYear == wy, Month %in% months) %>%ggplot(aes(x = logYield_big, y = logYield, color = date)) +geom_segment(aes(xend =c(tail(logYield_big, n =-1), NA), yend =c(tail(logYield, n =-1), NA)), arrow =arrow(length =unit(0.2, "cm")), color ="black") +geom_point() +geom_abline(intercept =0, slope =1, linetype ="dashed") +scale_color_gradientn(colors =cet_pal(90, name ="r1"), trans ="date") +xlim(-1,1.5) +ylim(-1.5,1.8) +#scale_color_scico(palette = "romaO") +xlab("log(Yield, mm) at reference gage") +ylab("log(Yield, mm) at headwater gage") +# geom_text(data = annotations, aes(x = xpos, y = ypos, label = annotateText), hjust = "inward", vjust = "inward") +annotate(geom ="text", x =-Inf, y =Inf, label =paste(mysite, ", WY ", wy, sep =""), hjust =-0.1, vjust =1.5) +theme_bw() +theme(panel.grid.major =element_blank(), panel.grid.minor =element_blank(),panel.background =element_rect(fill ="grey85"),axis.title =element_blank()) +theme(plot.margin =margin(0.1,0.1,0,0, "cm")) )}
Plot example sites and years. Generally, in rain-dominated basins the East (top two rows), we see relatively little hysteresis/non-stationarity in the relationship between streamflow in headwaters and at reference gages. In contrast, in snowmelt-dominated basins of the Rocky Mountains, we see much stronger hysteresis/non-stationarity in the relationship between streamflow in headwaters and at reference gages, but this varies considerably among locations.
What if we just consider the summer (low flow) period, July - September? In some ways, we see an opposite pattern relative to that describe above. In that we see greater hysteretic behavior in rain-dominated basins (driven by frequent summer storms and lagged runoff response) and less hysteretic behavior in snow-dominated basins, as all streams are in recession from the spring snowmelt peak. However, in general, we see greater divergence from a 1:1 relationship in snowmelt vs rain-dominated basins.
# A tibble: 87 × 7
subbasin site_name WaterYear freq meanpropyield meanhyst logmeanhyst
<chr> <chr> <dbl> <int> <dbl> <dbl> <dbl>
1 Big Creek Big Creek NWIS 2019 2 0.435 2.02 0.703
2 Big Creek Big Creek NWIS 2020 3 0.294 0.954 -0.0473
3 Big Creek Big Creek NWIS 2021 6 0.143 0.878 -0.130
4 Big Creek Big Creek NWIS 2022 7 0.134 0.746 -0.294
5 Big Creek Hallowat Creek… 2020 2 0.465 0.868 -0.141
6 Big Creek Hallowat Creek… 2022 6 0.162 1.05 0.0452
7 Big Creek NicolaCreek 2019 2 0.284 3.96 1.38
8 Big Creek WernerCreek 2019 2 0.407 1.84 0.608
9 Big Creek WernerCreek 2020 4 0.202 1.43 0.358
10 Coal Creek CycloneCreekUp… 2019 2 0.436 2.84 1.04
# ℹ 77 more rows
Characterize sites/subbasins along axes of event frequency and magnitude (mean annual proportion of flow within event).
Code
hull <- temp %>%group_by(subbasin) %>%slice(chull(freq, meanpropyield))temp %>%ggplot(aes(x = freq, y = meanpropyield)) +#geom_polygon(data = hull, aes(fill = subbasin), alpha = 0.5) +#geom_smooth(color = "black", method = "lm") +geom_point(aes(color = subbasin)) +xlab("Events per year") +ylab("Proportion of annual yield in event (mean over events)") +theme_bw() +theme(panel.grid.major =element_blank(), panel.grid.minor =element_blank())
Plot the mean annual magnitude (absolute value) of event-specific hysteresis by event frequency (events per year), with LOESS smoothing.
Code
p1 <- temp %>%ggplot(aes(x = freq, y = (meanhyst))) +geom_smooth(color ="black") +#geom_smooth(color = "black", method = "glm", formula = y~x, method.args = list(family = gaussian(link = 'log'))) +geom_point(aes(color = subbasin)) +xlab("Events per year") +ylab("Mean annual magnitude of hysteresis") +theme_bw() +theme(panel.grid.major =element_blank(), panel.grid.minor =element_blank())p2 <- temp %>%ggplot(aes(x = meanpropyield, y = (meanhyst))) +geom_smooth(color ="black") +#geom_smooth(color = "black", method = "glm", formula = y~x, method.args = list(family = gaussian(link = 'log'))) +geom_point(aes(color = subbasin)) +xlab("Proportion of annual yield in event") +ylab("Mean annual magnitude of hysteresis") +theme_bw() +theme(panel.grid.major =element_blank(), panel.grid.minor =element_blank())ggarrange(p1, p2, nrow =1, common.legend =TRUE, legend ="right")
Same as above but plot on log scale (magnitude):
Code
p1 <- temp %>%ggplot(aes(x = freq, y = logmeanhyst)) +geom_smooth(color ="black", method ="lm") +geom_point(aes(color = subbasin)) +xlab("Events per year") +ylab("(log) Mean annual magnitude of hysteresis") +theme_bw() +theme(panel.grid.major =element_blank(), panel.grid.minor =element_blank())p2 <- temp %>%ggplot(aes(x = meanpropyield, y = logmeanhyst)) +geom_smooth(color ="black", method ="lm") +geom_point(aes(color = subbasin)) +xlab("Proportion of annual yield in event") +ylab("(log) Mean annual magnitude of hysteresis") +theme_bw() +theme(panel.grid.major =element_blank(), panel.grid.minor =element_blank())ggarrange(p1, p2, nrow =1, common.legend =TRUE, legend ="right")
Replace regression line with convex hulls
Code
hull <- temp %>%group_by(subbasin) %>%slice(chull(freq, logmeanhyst))p1 <- temp %>%ggplot(aes(x = freq, y = logmeanhyst)) +geom_polygon(data = hull, aes(fill = subbasin), alpha =0.4) +geom_point(aes(color = subbasin)) +xlab("Events per year") +ylab("(log) Mean annual magnitude of hysteresis") +theme_bw() +theme(panel.grid.major =element_blank(), panel.grid.minor =element_blank())hull <- temp %>%group_by(subbasin) %>%slice(chull(meanpropyield, logmeanhyst))p2 <- temp %>%ggplot(aes(x = meanpropyield, y = logmeanhyst)) +geom_polygon(data = hull, aes(fill = subbasin), alpha =0.4) +geom_point(aes(color = subbasin)) +xlab("Proportion of annual yield in event") +ylab("(log) Mean annual magnitude of hysteresis") +theme_bw() +theme(panel.grid.major =element_blank(), panel.grid.minor =element_blank())ggarrange(p1, p2, nrow =1, common.legend =TRUE, legend ="right")
Alternatively, plot frequency by magnitude and with point color/size. I don’t think this tells the story as well as the convex hull plots.
Code
temp %>%ggplot(aes(x = meanpropyield, y = freq)) +# geom_polygon(data = hull, aes(fill = subbasin), alpha = 0.5) +geom_point(aes(color = subbasin, size = logmeanhyst)) +scale_size_continuous(range =c(0.1,5)) +xlab("Proportion of annual yield in event") +ylab("Events per year") +theme_bw() +theme(panel.grid.major =element_blank(), panel.grid.minor =element_blank())
Code
temp %>%ggplot(aes(x = meanpropyield, y = freq)) +# geom_polygon(data = hull, aes(fill = subbasin), alpha = 0.5) +geom_point(aes(color = logmeanhyst), size =2) +xlab("Proportion of annual yield in event") +ylab("Events per year") +theme_bw() +theme(panel.grid.major =element_blank(), panel.grid.minor =element_blank())
11.3.3.3 Site-year specific
Conduct baseflow separation, event delineation, and dynamic time warping as above, but only for a single site year. For troubleshooting and data visualization
Purpose: Quantify the suitability of existing modeling techniques for predicting streamflow in headwater systems.
Approach:
Download monthly Stream Stats, PRMS (for the Donner-Blitzen only), and UM’s neural net streamflow estimates for each site
Use NSE (Nash-Sutcliffe efficiency) to compare the performance of existing tools. How does this change as a function of basin size and time scale of data aggregation (e.g., daily to monthly)?
11.4.1 USGS Stream Stats
11.4.2 PRMS (DB)
11.4.3 UM Climatology
Pull HUC-10 streamflow predictions from Montana Climate Office’s (University of Montana) Streamflow API
Get HUC-10 watershed codes
Code
myhucs <-c()for (i in1:dim(siteinfo_sp)[1]) { myhucs[i] <-get_huc(AOI = siteinfo_sp[i,], type ="huc10")$huc10 }siteinfo <- siteinfo %>%mutate(huc10 = myhucs)myhucs <-unique(myhucs)length(myhucs)
[1] 16
Query UM Climatology
Code
request = httr::GET(# can replace this with /predictions/raw, the only query parameter that isn't shared is aggregations."https://data.climate.umt.edu/streamflow-api/predictions/",query =list(locations =paste(myhucs, collapse =","),date_start ="2015-01-01",date_end ="2025-01-01",aggregations ="mean", as_csv =TRUE,units ="mm" ))umpreds <- httr::content(request)umpreds <- umpreds %>%rename(huc10 = location)print(umpreds)
# A tibble: 58,464 × 5
huc10 version date metric value
<chr> <chr> <date> <chr> <dbl>
1 0108020106 vPUB2025 2015-01-01 mean 2.14
2 0108020106 vPUB2025 2015-01-02 mean 1.86
3 0108020106 vPUB2025 2015-01-03 mean 1.93
4 0108020106 vPUB2025 2015-01-04 mean 4.00
5 0108020106 vPUB2025 2015-01-05 mean 4.04
6 0108020106 vPUB2025 2015-01-06 mean 3.07
7 0108020106 vPUB2025 2015-01-07 mean 2.43
8 0108020106 vPUB2025 2015-01-08 mean 2.16
9 0108020106 vPUB2025 2015-01-09 mean 2.03
10 0108020106 vPUB2025 2015-01-10 mean 1.90
# ℹ 58,454 more rows
dat_umpred %>%filter(site_name =="Jimmy Brook") %>%select(date, Yield_mm, value) %>%dygraph() %>%dySeries("Yield_mm", color ="black") %>%dySeries("value", color ="red") %>%dyRangeSelector()
11.4.3.1 Staunton 06
Code
dat_umpred %>%filter(site_name =="Staunton River 06") %>%select(date, Yield_mm, value) %>%dygraph() %>%dySeries("Yield_mm", color ="black") %>%dySeries("value", color ="red") %>%dyRangeSelector()
11.4.3.2 Hallowatt Creek NWIS
Code
dat_umpred %>%filter(site_name =="Hallowat Creek NWIS") %>%select(date, Yield_mm, value) %>%dygraph() %>%dySeries("Yield_mm", color ="black") %>%dySeries("value", color ="red") %>%dyRangeSelector()
11.4.3.3 SF Spread Ck Lower
Code
dat_umpred %>%filter(site_name =="SF Spread Creek Lower") %>%select(date, Yield_mm, value) %>%dygraph() %>%dySeries("Yield_mm", color ="black") %>%dySeries("value", color ="red") %>%dyRangeSelector()
11.4.3.4 Dugout Creek
Code
dat_umpred %>%filter(site_name =="Dugout Creek") %>%select(date, Yield_mm, value) %>%dygraph() %>%dySeries("Yield_mm", color ="black") %>%dySeries("value", color ="red") %>%dyRangeSelector()
11.4.3.5 DB ab Indian NWIS
Code
dat_umpred %>%filter(site_name =="Donner Blitzen ab Indian NWIS") %>%select(date, Yield_mm, value) %>%dygraph() %>%dySeries("Yield_mm", color ="black") %>%dySeries("value", color ="red") %>%dyRangeSelector()
:::
NSE ratings per Moriasi et al. “Model evaluation guidelines for systematic quantification of accuracy in watershed simulations.” Transactions of the ASABE 50.3 (2007): 885-900.
Very good: 0.75-1.00
Good: 0.65-0.75
Satisfactory: 0.50-0.65
Unsatisfactory: <0.50
Note that there is no effort to ensure consistant data availability among sites/basins/years. Would it be better to restrict these?
Demonstrate how drought-related low flow conditions manifest differently in streams across headwater networks.
Using site-specific low flow thresholds derived from contemporary data (sensu Hammond et al. 2022), show how streamflow drought duration and deficit vary among headwater streams and relative to big G (heatmaps and barplots)
Explore how network heterogeneity changes with threshold magnitude and among years that differ in regional water availability (scatterplots)
Purpose: Demonstrate spatial variation in drought-related low flow conditions across headwater stream networks.
Approach:
Derive site-specific low flow thresholds from contemporary data (sensu Hammond et al. 2022).
Use heatmaps and barplots to show duration and severity of low flow conditions and variation among sites and relative to big G.
Use scatterplots (or something similar) to explore how network heterogeneity changes with threshold magnitude and among years that differ in regional water availability
11.5.1 Low flow thresholds
11.5.1.1 Basin scale
Generate fixed and time varying (by day of year) drought/low flow thresholds from long-term (1970-2025) big G streamflow data. Quantiles in ~0.05 increments from 0.02 to 0.50.
Drought/low flow delineation is somewhat complicated by the fact that some streams simply have greater yield than others. For example, at groundwater-dominated sites, the above approach will never detect low flow conditions based on big G thresholds, but this doesn’t mean that flow at that site isn’t lower than normal (for that site). This is most obvious in the Snake River basin, where NF Spread Creek Upper never experiences drought (because this is presumably a gaining reach) and Rock and Grouse Creeks are in a perpetual state of drought (presumable these are losing reaches). This is a classic “At which level of organization do I standardize my data?” question: are general differences in flow volume among sites signal or noise? But perhaps more importantly, this is a question of “what is drought?” Is drought relative to some larger regional metric (e.g., big G)? Or is it a local phenomenon, where the specifics of individual streams and reaches matter.
For each site individually, generate (fixed) drought/low flow thresholds using the same quantiles same as above: ~0.05 increments from 0.02 to 0.50. Restrict data to selected basins, sites, and years with (nearly) complete summer (July, August, September) data over the selected periods/locations. (Standardization needs to be done over comparable time periods, at least among sites within basins).
Require 95% data availability across all water years for site to be included!
Organize data, get site-level low flow threshold values, and denote drought periods
Show proportion of days (July - September) below different low flow thresholds (derived from long-term Big G data) for each site during a relatively wet year and a dry year. Then, for each year, plot the relationship between the among site (little g’s only) standard deviation of low flow duration and the low flow threshold used to calculate duration
durationplotfun(subbas ="Donner Blitzen", bigG ="Donner Blitzen River nr Frenchglen NWIS", months =c(7:9), wateryears =c(2022, 2020))
Deficit
Show total drought deficit (mm) relative to different low flow thresholds (derived from long-term Big G data) for each site during a relatively wet year and a dry year. Then, for each year, plot the relationship between the among site (little g’s only) standard deviation of deficit and the low flow threshold used to calculate deficit
Show proportion of days (July - September) below different low flow thresholds (derived from temporally restricted, site-specific data) for each site during a relatively wet year and a dry year. Then, for each year, plot the relationship between the among site (little g’s only) standard deviation of low flow duration and the low flow threshold used to calculate duration
durationplotfun_sub(subbas ="Donner Blitzen", bigG ="Donner Blitzen River nr Frenchglen NWIS", months =c(7:9), wateryears =c(2022, 2020))
Deficit
Show total drought deficit (mm) relative to different low flow thresholds (derived from long-term Big G data) for each site during a relatively wet year and a dry year. Then, for each year, plot the relationship between the among site (little g’s only) standard deviation of deficit and the low flow threshold used to calculate deficit
deficitplotfun_sub(subbas ="Donner Blitzen", bigG ="Donner Blitzen River nr Frenchglen NWIS", months =c(7:9), wateryears =c(2022, 2020))
11.6 Boxes
11.6.1 Box 1
Purpose: Show what high-resolution temporal data (hourly) reveals about network diversity in streamflow response to individual storms (peak flow magnitude and timing and recession rates) and during low flow (diel fluctuations)
11.6.2 Box 2
The Wedge Model for the West Brook
Purpose: At coarser time scales (summarized by event/baseflow periods), show how streamflow heterogeneity expands and contracts during wet to dry periods.
11.6.3 Box 3
Purpose: Show what high-resolution spatial data reveals about network diversity in streamflow at a single point in time.
11.6.4 Box 4
Purpose: Explore the effect of groundwater on relative summer (July-September) water availability.
Load PASTA daily derived parameters: summarize as July-September site-specific means (across all years)
Plot the relationship between standardized annual summer mean discharge and amplitude ratio from PASTA, where lower amplitude ratio values are indicative of greater groundwater availability. Mean flow for each site is standardized by year to remove interannual variation in climate/regional water availability
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Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
Error : There are missing values in the series.
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Error : There are missing values in the series.
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Code
# summarize monthly mean yield by site, yeartt <- dat_clean %>%mutate(basin =ifelse(subbasin =="Duck Creek", "Shields River", basin)) %>%filter(!is.na(logYield), designation =="little") %>%group_by(region, basin, subbasin, site_name, designation, CalendarYear, Month) %>%summarize(meanQ =mean(logYield, na.rm =TRUE), nobs =n()) %>%ungroup() %>%filter(nobs >=27) %>%left_join(drought) # calculate correlationsmylist_dsci_slope <-list()mylist_dsci_pval <-list()mylist_dsci_rho <-list()mylist_spi_slope <-list()mylist_spi_pval <-list()mylist_spi_rho <-list()# list of sites to iterate oversites <-unique(tt$site_name)for(i in1:length(sites)) { d <- tt %>%filter(site_name == sites[i]) mymat_dsci_slope <-matrix(data =NA, nrow =12, ncol =24) mymat_dsci_pval <-matrix(data =NA, nrow =12, ncol =24) mymat_dsci_rho <-matrix(data =NA, nrow =12, ncol =24) mymat_spi_slope <-matrix(data =NA, nrow =12, ncol =24) mymat_spi_pval <-matrix(data =NA, nrow =12, ncol =24) mymat_spi_rho <-matrix(data =NA, nrow =12, ncol =24)for(j in1:12) {for(k in1:24) {if(nrow(d %>%filter(Month == j)) <3) next# DSCI d2 <- d %>%filter(Month == j) %>%select(meanQ, paste("dsci_monthly_", k, sep =""))## slope and p-valuetry(mylm <-lm(unlist(d2[,1]) ~unlist(d2[,2])), silent =TRUE)try(mymat_dsci_slope[j,k] <-summary(mylm)$coefficients[2,1], silent =TRUE)try(mymat_dsci_pval[j,k] <-summary(mylm)$coefficients[2,4], silent =TRUE)## pearons r correlationtry(mymat_dsci_rho[j,k] <-cor(d2[,1], d2[,2], method ="pearson", use ="complete.obs"), silent =TRUE)# SPI d2 <- d %>%filter(Month == j) %>%select(meanQ, paste("spi_", k, sep =""))## slope and p-valuetry(mylm <-lm(unlist(d2[,1]) ~unlist(d2[,2])), silent =TRUE)try(mymat_spi_slope[j,k] <-summary(mylm)$coefficients[2,1], silent =TRUE)try(mymat_spi_pval[j,k] <-summary(mylm)$coefficients[2,4], silent =TRUE)## pearons r correlationtry(mymat_spi_rho[j,k] <-cor(d2[,1], d2[,2], method ="pearson", use ="complete.obs"), silent =TRUE) } } mylist_dsci_slope[[i]] <- mymat_dsci_slope mylist_dsci_pval[[i]] <- mymat_dsci_pval mylist_dsci_rho[[i]] <- mymat_dsci_rho mylist_spi_slope[[i]] <- mymat_spi_slope mylist_spi_pval[[i]] <- mymat_spi_pval mylist_spi_rho[[i]] <- mymat_spi_rhoprint(i)}# generate plots/heatmaps of correlationn <-100for(i in1:length(sites)) {# streamflow mean ~ DSCIjpeg(paste("./Climate Sensitivity/Climate sensitivity plots/Streamflow_DSCI_correlation_TimeVarying_", "site", i, "_mean.jpg", sep =""), height =6, width =7, units ="in", res =500)filled.contour(x =1:24, y =1:12, z =t(corlist_dsci_mean[[i]]), levels =seq(from =-1, to =1, length = n+1), col =hcl.colors(n, "PRGn"),plot.title =title(main = sites[i], xlab ="DSCI - accumulation time scale (months)", ylab ="Month"),plot.axes = { axis(1, at =seq(from =1, to =23, by =2))axis(2, at =1:12, labels =c("J", "F", "M", "A", "M", "J", "J", "A", "S", "O", "N", "D")) contour(x =1:24, y =1:12, z =t(corlist_dsci_mean[[i]]), add =TRUE, labcex =1, levels =seq(from =-1, to =1, length =11)) })dev.off()# streamflow mean ~ SPIjpeg(paste("./Climate Sensitivity/Climate sensitivity plots/Streamflow_SPI_correlation_TimeVarying_", "site", i, "_mean.jpg", sep =""), height =6, width =7, units ="in", res =500)filled.contour(x =1:24, y =1:12, z =t(corlist_spi_mean[[i]]), levels =seq(from =-1, to =1, length = n+1), col =hcl.colors(n, "PRGn"),plot.title =title(main = sites[i], xlab ="SPI - accumulation time scale (months)", ylab ="Month"),plot.axes = { axis(1, at =seq(from =1, to =23, by =2))axis(2, at =1:12, labels =c("J", "F", "M", "A", "M", "J", "J", "A", "S", "O", "N", "D")) contour(x =1:24, y =1:12, z =t(corlist_spi_mean[[i]]), add =TRUE, labcex =1, levels =seq(from =-1, to =1, length =11)) })dev.off()# streamflow minimum ~ DSCIjpeg(paste("./Climate Sensitivity/Climate sensitivity plots/Streamflow_DSCI_correlation_TimeVarying_", "site", i, "_min.jpg", sep =""), height =6, width =7, units ="in", res =500)filled.contour(x =1:24, y =1:12, z =t(corlist_dsci_min[[i]]), levels =seq(from =-1, to =1, length = n+1), col =hcl.colors(n, "PRGn"),plot.title =title(main = sites[i], xlab ="DSCI - accumulation time scale (months)", ylab ="Month"),plot.axes = { axis(1, at =seq(from =1, to =23, by =2))axis(2, at =1:12, labels =c("J", "F", "M", "A", "M", "J", "J", "A", "S", "O", "N", "D")) contour(x =1:24, y =1:12, z =t(corlist_dsci_min[[i]]), add =TRUE, labcex =1, levels =seq(from =-1, to =1, length =11)) })dev.off()# streamflow minimum ~ SPIjpeg(paste("./Climate Sensitivity/Climate sensitivity plots/Streamflow_SPI_correlation_TimeVarying_", "site", i, "_min.jpg", sep =""), height =6, width =7, units ="in", res =500)filled.contour(x =1:24, y =1:12, z =t(corlist_spi_min[[i]]), levels =seq(from =-1, to =1, length = n+1), col =hcl.colors(n, "PRGn"),plot.title =title(main = sites[i], xlab ="SPI - accumulation time scale (months)", ylab ="Month"),plot.axes = { axis(1, at =seq(from =1, to =23, by =2))axis(2, at =1:12, labels =c("J", "F", "M", "A", "M", "J", "J", "A", "S", "O", "N", "D")) contour(x =1:24, y =1:12, z =t(corlist_spi_min[[i]]), add =TRUE, labcex =1, levels =seq(from =-1, to =1, length =11)) })dev.off()}# plot raw dataplot(meanQ ~ spi_9, tt %>%filter(site_name =="Big Creek NWIS", Month ==10))plot(z_flow_mean_monthly ~ spi_7, dat3 %>%filter(site_name =="Donner Blitzen River nr Frenchglen NWIS", month ==6))filled.contour(x =1:24, y =1:12, z =t(mylist_dsci_slope[[1]]), levels =seq(from =-1, to =1, length =50), col =hcl.colors(50, "PRGn"),plot.title =title(main = sites[i], xlab ="DSCI - accumulation time scale (months)", ylab ="Month"),plot.axes = { axis(1, at =seq(from =1, to =23, by =2))axis(2, at =1:12, labels =c("J", "F", "M", "A", "M", "J", "J", "A", "S", "O", "N", "D")) contour(x =1:24, y =1:12, z =t(mylist_dsci_slope[[i]]), add =TRUE, labcex =1, levels =seq(from =-1, to =1, length =11)) })filled.contour(x =1:24, y =1:12, z =t(mylist_spi_pval[[1]]), levels =seq(from =0, to =1, length =100), col =hcl.colors(100, "Blues"))filled.contour(x =1:24, y =1:12, z =t(mylist_spi_slope[[1]]), levels =seq(from =-1, to =1, length =100), col =hcl.colors(100, "PRGn"))